The ball used in a golf tournament have diameters of 4.2cm and 4.4cm.what is the difference in the surface area between the largest and smallest golf ball
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Step-by-step solution
6 stepsLet's find the difference in surface area between the two golf balls.
Determine the radii for both golf balls.
For the smaller ball (diameter = 4.2 cm):
r₁ = 4.2 cm / 2 = 2.1 cm
For the larger ball (diameter = 4.4 cm):
r₂ = 4.4 cm / 2 = 2.2 cmWrite the formula for the surface area of a sphere.
Surface Area (A) = 4πr²
Calculate the surface area for the smaller ball (A₁).
A₁ = 4 × π × (2.1 cm)²
A₁ = 4 × π × 4.41 cm²
A₁ = 17.64π cm²Calculate the surface area for the larger ball (A₂).
A₂ = 4 × π × (2.2 cm)²
A₂ = 4 × π × 4.84 cm²
A₂ = 19.36π cm²Find the difference in surface area.
Difference = A₂ - A₁
Difference = 19.36π cm² - 17.64π cm²
Difference = (19.36 - 17.64)π cm²
Difference = 1.72π cm²Calculate the numerical value (using π ≈ 3.14159).
Difference ≈ 1.72 × 3.14159 cm²
Difference ≈ 5.404 cm²The difference in surface area between the largest and smallest golf ball is approximately 5.40 cm².
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